Question

Iron pyrites have the formula$Fe{S_2}.\left( {Fe = 56;S = 32} \right)$ . What is the mass of sulfur contained in $30$ grams of pyrites?
A. \[16{\rm{ }}g\]
B. \[{\rm{32 }}g\]
C. \[{\rm{20 }}g\]
D. \[{\rm{24 }}g\]

Answer 1

Hint: Mass of an element in a given compound can be determined by using its mass percent which in turn can be calculated from the chemical formula and molar mass.

Complete step by step answer:
Firstly, we need to calculate the mass percent of sulfur in the iron pyrites:
Chemical formula of a compound gives the number of atoms of each element present in a molecule/formula unit of the compound. We can use the chemical formula to calculate the molar mass of the compound by using the number of atoms and molar masses for each element.
As per the formula$Fe{S_2}$, one mole of iron pyrite contains one mole of iron and two moles of sulfur. So, the molar mass of iron pyrites would be the sum of mass of one mole of iron and mass of two moles of sulfur. We can calculate the molar mass of iron pyrites by using the given values as follows:
$\begin{array}{c}
{M_{Fe{S_2}}} = \left( {1 \times {M_{Fe}}} \right) + \left( {2 \times {M_S}} \right)\\
 = \left( {1 \times 56{\rm{ g/mol}}} \right) + \left( {2 \times 32{\rm{ g/mol}}} \right)\\
 = {\rm{120 g/mol}}
\end{array}$
Mass percent of an element in a compound is the mass of that element present in $100\;g$ of that compound expressed as percent. We can write it mathematically:
${\rm{mass\% of element}} = \left( {\dfrac{{{\rm{mass of element in one mole of the compound}}}}{{{\rm{molar mass of the compound}}}}} \right) \times 100\% $
Here, we can calculate the mass percent of sulfur as follows:
\[\begin{array}{c}
{\rm{mass\% of }}S{\rm{ in }}Fe{S_2} = \left( {\dfrac{{{\rm{mass of }}S{\rm{ in one mole of }}Fe{S_2}}}{{{\rm{molar mass of }}Fe{S_2}}}} \right) \times 100\% \\
 = \left( {\dfrac{{2 \times 32{\rm{ g/mol}}}}{{{\rm{120 g/mol}}}}} \right) \times 100\% \\
 = {\rm{53}}{\rm{.33\% }}
\end{array}\]
So, now we know that there is \[{\rm{53}}{\rm{.33 }}g\] of sulfur present in $100\;g$ of iron pyrites. We can convert this into the unit factor and write:
\[\dfrac{{{\rm{53}}{\rm{.33 }}g\;S}}{{100\;g\;Fe{S_2}}}\]
Finally, we can determine the mass of sulfur contained in $30$ grams of pyrites by using the above unit factor as follows:
Hence, the mass of sulfur contained in $30$ grams of pyrites is calculated to be \[16{\rm{ }}g\] which makes option A to be the correct one.

Note:
We have to be careful with the units while doing the calculations as the numerical values of formula mass and molar mass are the same but their units are different.